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NOTES AND EXERCISES 



ox 



SURVEYING- 



FOR THE USE OF STUDENTS IN 



KENYON COLLEGE. 



BY 



V 



ELI T. TAPPAN, LL.D., 

PROFESSOR OF MATHEMATICS. 




GAMBLER, 0.: 

EDMONDS & HUNT, PRINTERS. 

1878. 



ft 



Copyright, 1878, by ELI T. TAPPAN. 



•T/f 



S-38JW 



<0 



PREFACE 



This is not a treatise on Surveying ; it is only some notes and 
exercises for the use of college students. Many things are omitted 
which I expect to give by oral instruction in the class room or in 
the field. 

However, it is not my intention, either by these notes or 
otherwise, to attempt to make professional engineers of students, 
in the regular college work. That belongs to a professional 
school. 

It is a part of my design to enforce upon the students a com- 
parison of the two modes of gaining knowledge — by observation, 
and by calculation. Also, to lead them to consider the subject 
of probable error in results. E. T. T. 

Gambier, Ohio, { 

February 19, 1878. j 



SURVEYING. 



Surveying is a branch of applied mathematics which has 
for its object the measuring the earth's surface or parts of it, 
including heights, distances, and areas, and representing the 
same by a plat or chart. 

Plane surveying is that in which small portions of the earth's 
surface are regarded as parts of a plane. Topographical sur- 
veying consists in the measurement and exact delineation of a 
place, including variations of level. Geodetic surveying, or 
geodesy, relates to the whole earth or to large portions of it, 
taking into consideration the curvature of the surface. 

Surveying is to be distinguished, on the one hand, from 
mensuration, which is applied to measuring smaller objects, 
and on the other hand, from astronomy, which relates to the 
sizes and distances of the heavenly bodies. 

All measurement consists in two operations — observation 
and calculation. The results of observation are more or less 
imperfect, depending upon the keenness of the senses and 
manual skill. Calculation may be made to any required de- 
gree of accuracy. 

OBSERVATION. 

Observations in surveying consist in measuring either dis- 
tances or angles, and these quantities, of both kinds, are ob- 
served by the direct application of a standard. In geodesy, 
however, as in astronomy, time is an object of direct obser- 
vation. 



() SURVEYING. 

The standard measures of length are the meter and the 
foot. The meter is used in the geodetic surveys made by the 
government. The foot, divided decimally, is generally used 
by railway engineers. 

The meter, when first adopted by the French, was suppo- 
sed to be one ten-millionth part of the distance on the surface 
of the earth from the equator to the pole. More accurate 
geodetic surveys have shown that the meter is a little shorter 
than this, and it is suspected that the distance varies in differ- 
ent longitudes. As the meter has been adopted by nearly all 
enlightened nations as the primary unit for all measures, it is 
not probable that any effort will be made to correct the error. 

The standard meter is the actual bar of platinum kept by the 
French government. The standard yard is the actual bar kept 
by the British government. The government of the United 
States has very accurate copies of these, but it is said that the 
yard exceeds the British standard by nearly one-thousandth of 
an inch, and there is a smaller error in the meter. 

INSTRUMENTS OF LENGTH. 

M 

The surveyor's chain is four rods long, in one hundred links, 
but the instrument generally used is a half-chain. Railway 
engineers use a chain of one hundred feet. 

When the common surveyors chain is used, it is always 
for measuring horizontal distance, and the two ends must be 
held at the same level, whatever be the actual unevenness of 
the surface. Hence, it is necessary, in testing the length of the 
chain, to allow for the diminution in length caused by the 
sagging when suspended. It also becomes the rule that all 
chaining is done by the chain held up. Evidently, some skill 
is required to make uniform and correct measures of distance, 
in this way. Sometimes, on a steep hill side, it is necessary 
to use a smaller part of the chain. 

In using the eleven pins which are with the chain, observe 
these rules : — 1. But one pin at the beginning of the distance 
to be measured. 2. The chainman in advance takes ten pins. 



SURVEYING. i 

3. The pin at the rear must be taken up after the pin in ad- 
vance is fixed in its place, so that one pin is in place all the 
time. 

These rules are partial. Skill in the use of these anl all 
other instruments can only be acquired by practice, under the 
direction of a competent surveyor. 

The levelling staff is used for observing differences of 

CD O 

level, that is, vertical distance. The principal rule to be fol- 
lowed in its use is that it must be held as nearly vertical as 
possible. 

In the level, the parts to be noticed are : — 

1. The tripod ; 

2. The joint, parallel plates, and levelling screws ; 

3. The vertical axis, revolving beam and wyes; 

4. The telescope and spirit level ; and 

5. The adjustment for keeping the beam and telescope 

parallel to the spirit level. 

INSTRUMENTS OF DIRECTION. 

These are the compass of various kinds, the transit, the 
theodolite, and the sextant. 

The student is expected to become acquainted with thesi3 
instruments and their use, by studying the instruments them- 
selves under the direction of the teacher. 

The compass is used for measuring the horizontal angle 
which any line makes with the meridian, that is, an angle 
having its arms in the plane of the horizon, and one of them 
due North and South. The engineer's transit is used for 
measuring any horizontal angle, with greater accuracy than is 
aimed at with the compass. The theodolite is used for measur- 
ing horizontal and vertical angles. A vertical angle is one 
having its arms in a vertical plane, that is, perpendicular to 
the horizon, one of them being also in the plane of the hori- 
zon. It is an angle of elevation or of depression, according 
as one arm is above or below the horizon. The sextant is 
used for measuring angles in any plane whatever, usually for 
astronomical purposes. 



b SURVEYING. 

The parts of a compass, to be noticed, are : The staff, the 
joint, the box, the circle, the needle, and the sights. Some 
compasses have a spirit level. The solar compass has an ap- 
paratus for determining the true meridian by observations of 
the sun. 

In a transit there are be noticed : — 

1. The tripod and the plummet ; 

2. The joint, parallel plates, and levelling screws ; 

3. The vertical axis, with its clamp ; 

4. The graduated circle and vernier plate ; and 

5. The spirit level and the telescope. 

The theodolite has the same things and a vertical gradua- 
ted circle and vernier. 

The vernier is an ingenious contrivance for more accurate 
measurement, which is attached to all kinds of instruments. 
It is fixed to that part of the instrument upon which or by 
which the observation is made, that is, to the telescope in 
the transit and theodolite, and to the movable part of the 
levelling staff. A portion of it which moves along the 
principal scale is so divided that n divisions of the vernier are 
equal to n — 1 or n + 1 of the smallest divisions of the scale. 
The zero point of the vernier indicates the position on the 
scale which is to be ascertained. If this exactly coincides 
with a dividing mark, then the measure is read on the princi- 
pal scale and no reading of the vernier is required ; but when 
the zero point of the vernier comes between two marks on the 
scale, the main scale is first read and there must be added an 
amount ascertained by the vernier. The amount to be added 
is indicated by that division mark on the vernier which exact- 
ly coincides with one on the scale. If this mark is the mt)\ 
from zero, there must be added m times the rath part of the 
quantity indicated by one of the smallest divisions on the 
principal scale. This nth part is called the least count of the 
vernier. 

The explanation of the principle of the vernier is left to 
the student, an easy task, with the instrument in his hands. 
(In the theodolite of K. 0., n is 30, and the least count is one 



SURVEYING. 9 

minute of arc. In the levelling staff, n is 10, and the least 
count is one-thousanclth of a foot. ) 

Students should be cautioned not to abuse instruments. 
Treat every instrument gently ; do not use force, particularly 
on the levelling screws. 

Exercises.— 1. Make a drawing and description of each 
instrument used by the class, specifying the use and purpose of 
each part. 

2. Measure with the theodolite, the three angles of a tri- 
angle. The difference between the sum and two right angles 
shows the amount of error. 



INSTRUMENTS FOR PLATTING. 

Every student should be provide.! with a scale, a protrac- 
tor, and a pair of dividers. 

Instruction in the use of these instruments is omitted here, 
as it can be given better by the teacher, with the instruments 
in hand. 

Exercises. — 1. Draw any triangle on paper; measure each 
angle with the protractor. The difference between the sum and 
two right angles show T s the amount of error. 

2. Measure two sides ; from these and the angles calculate 
the other side ; then measure and compare. 

3. Make a plat of every w 7 ork done in the field. Make 
every plat to a certain scale, and write the scale on the margin. 

HEIGHTS AND DISTANCES. 

The solution of the principal problems of this class, by 
triangulation, is explained in the Trigonometry, Art. 875. 

In applying these methods in the field, the student should 
endeavor to measure every line in two independent ways- 
The less the discrepancy, the more accurate the work. 

The barometer is frequently used for measuring heights, 
particularly of mountains. This instrument is described in 
works on Physics. 



10 SURVEYING. 

LEVELLING. 

When great accuracy is required, as in mining and mak- 
ing railways and canals, differences of level are measured by 
the instrument called the level. 

Skill in the use of the level and staff are acquired only by 
practice. 

Some authors advise that the level should be at nearly 
equal distances from the preceding and. following station, in 
order to avoid the error arising from the curvature of the 
earth's surface. A little observation and calculation will show 
that no ordinary instrument is sufficiently accurate to detect 
any error that could be attributed to this cause. At the dis- 
tance of 200 feet the deflection is less than one-thousandth of 
a foot. 

When the object of levelling is to ascertain the difference 
in level of two points, and no plat is to be made, then the 
notes only record the " back sights and fore sights " in two 
columns. Thus, to find the height of Rosse porch above 
Ascension door sill : 

Back Sights. Fore Sights. 

1st 3.496 feet. 2.351 feet. 

2nd 9.620 0.705 

3rd 10.721 4.388 

23.837 7.444 
7.444 

16.393 feet. 

When a profile of a road is to be made, the level at every 
100 feet, or other certain distance, should be recorded. The 
plat of the profile of a road usually is distorted, having a larger 
scale for the heights than for the horizontal distance. 

A topographical map of a place, has contour lines, that is, 
lines showing where level planes would intersect the actual 
surface, these planes being at regular intervals of height above 
some established base. The proper location of such lines is 
found by levelling, the details of the work depending upon 
the peculiarities of each locality. 



SURVEYING. 11 

Exercises. — 1. Ascertain the height of a hill by levelling 
over two different routes. Compare, and discuss the probable 
error. 

2. Ascertain the same height by triangulation, by at least 
two sets of observations and calculations.. Compare as before. 

3. Determine the relative degrees of accuracy of the two 
methods. 

4. Make similar exercises in the measure of the length of a 
line, by chaining and by triangulation, to determine the proba- 
ble error of each method, and relative accuracy of the two 
methods. 

AREA OF LAND. 

In determining the area of Ian 1, the inequalities of the 
surface are disregarded ; the area to be measured is that of the 
horizontal plane within the same boundaries. The length of 
a line is the horizontal distance between its extremities, which 
may be much less than the distance along the surface. The 
arms of every angle measured are horizontal lines. 

When a piece of land is in the shape of a square, a rectan- 
gle, a parallelogram, a triangle, a trapezoid, or any regular 
geometrical figure, the method of measuring its area consists 
in a simple application of the geometrical principle, and needs 
no further comment here. 

When the shape is that of a polygon, that is, when all the 
sides are straight, the usual method is by a system of triangks 
and trapezoids. When some of the boundaries consist of ir- 
regular curves, as the bank of a stream, the error may be di- 
minished at will by substituting straight lines nearly coincident 
with the curve. Sometimes it is more convenient to separate 
such a tract into two, surveying the more irregular part by 
itself. The advantage of this is in excluding many small sides 
from the calculation. 

The field notes of a survey are the record, male on the 
spot, of the bearing and distance of each side of the field. 
For example the following are the field notes of the survey of 
Jan's Lot a six sided field : 



12 





SURVEYING. 






Bearings. 


Distances. 


1. 


S. 89° E. 


5.335 


2. 


N. 2Q° E. 


1.60 


3. 


N. 55° W. 


4.57 


4. 


S. 20° W. 


1.842 


5. 


S. 87° W. 


1.593 


6. 


S. 2° W. 


2.15 



The bearing of a line is the angle, not over 90°, which the 
line makes with the magnetic meridian, the letters indicating 
in which quarter of the compass. The nature and amount 
of the difference between the magnectic and the true meridian 
should be known to every surveyor. The explanation of these 
belongs to the sciences of Astronomy and Terrestrial Magnet- 
ism . 

The distance of a line or side of a field, is its length in 
chains. 

The degree of accuracy required depends entirely upon 
circumstances. Only very valuable land need be measured 
to a tenth of a link, as in the above notes. A good compass 
enables the observer to measure an angle within a half or 
even a quarter of a degree. 

The method of calculating the area is best explained by 
means of a plat ; but in practice, the plat may be made either 
before, or after the calculation. 

First make a line parallel to the side of the paper, for a 
prime meridian. This line should pass through either the 
easternmost or the westernmost corner of the plat. In this 
case, it is the western corner, A, that being the first station 
indicated by the field notes. 

With the protractor, make the angle BAS = 89°, 
that being the first bearing. Make its length according to the 
scale. Since the direction of the next side is 26° East of 
North, and the direction BA is 89° West of North, the an- 
gle ABC must be made 115°. Since the next direction is 
55° West of North and CB is 26° West of South, the angle 
BCD must be made 99°, that is 180° — (55°+26°). ^So 
on, for the angles at D, E, and F. The angle at each corner 
depends upon the preceding and the following bearing. It 
may be, 1. the sum of the bearings, or 2. the supplement of 



SURVEYING. 



13 



N 



Scile: M inch to the chain. 



E 



/ 



that sum, or 3. the difference of the bearings, or 4. the supple- 
ment of that difference. If the survey and drawing are 
accurate, the end of the last side falls upon the initial point A. 
From B, C, D, E, and F, let the perpendiculars BG, CH, 
DJ, EK, and FL fall on the prime meridian NS. (These 
are not given in the diagram, but should be made by the 
student.) These perpendiculars form the bases of four 
trapezoids and two triangles, the other sides of these figures 
are either sides of the iield or parts of the prime meridian. 
From the observed bearings and distances, we may calcu- 

CD J t> 

late the bases and altitudes, and thence the areas of all these 
figures : then subtracting the sum of the four areas which 
are outside of the field from the sum of the other two, which 
contain these four and the field, we have the area of the field. 
See the calculation on next page. 

The latitude of a side is the distance which one end is 
North or South of the other. Thus AG is the latitude of 
the side AB, FIG is the latitude of BC, etc. The latitude 
of a side is its projection on a meridian line ; also, it is the 
product of the distance by the cosine of the bearing. 

The departure of a line is the distanc3 which one end is 



u 



SURVEYING. 





Calculation 


of the Area. 






Latitudes. 


Departures. 


Correct 's 


Balanced. 


D.M.D. 


double Area 


North | South 


East. | West 


L | D. | 


Latitud's. | Departs 


North. | South 



1.438 
2.621 



14.059 



.093 



1.731 

.038 

2.149 



4.056 



Error 



5.334 
.701 



6.03, f 



Error 11 




3.744 
.636 

1.591 
.075 



-+ 6.338 
+ .702 
— 3.741 

.635 
1.590 

.074 



5.338 
J 1.378 
8.339 
3.963 
1.738 
.074 



20) 



16.3621 

21.8481 



38.210 
7.670 



30.54 



1.527 



.507 



6.860 
.144 
.159 

7.670 



East or West of the other. Thus GB is the departure of 
the side AB ; HC — GB is the departure of BC. etc. 
The departure of a side is its projection on a parallel of lati- 
tude ; also, it is the pro luct of the distance by the sine of the 
bearing. 

The latitudes and departures are ascertained by aid of a 
traverse table, which is a table of the latitudes and depart- 
ures for a unit of distance, for each half-degree of the quad- 
rant. The traverse table used by professional surveyors 
frequently gives the latitudes and departures for each quarter- 
degree, and with the multiples for the first nine digits. The 
one on page 18 is sufficient for learning the principle. 

The latitudes and departures are distinguished as North- 
ings, Southings, Eastings, or Westings, according to the 
bearings, and are placed in four separate columns. Evidently, 
if the survey and calculations are accurate, the sum of the 
northings must be equal to that of the southings, and the 
sum of the eastings to that of the westings. Perfect equality 
in these is not to be expected, for the observed facts are not 
perfect, the angles being rarely measured to less than the half- 
degree, and the sides to less than one link. Whether the error 
may be disregarded is a question of economy, that depends 
entirely upon the amount of the error and the value of the 
land. The probable amount of the error is found by multi- 
plying the sum of the northings by the error of departure, and 



SURVEYING. 15 

the sum of the eastings by the error of latitude, and taking 
the sura of these products. If the amount of land repre- 
sented by this sum is worth half the expense of a survey, the 
land should be re-surveyed. If the error is not too great, 
it should be distributed, so as to make the northings equal the 
southings, and the eastings equal the westings. 

When there is no reason to suspect that the error belongs 
more to one side than to an other, it may be distributed in 
proportion to the distance. For example, in the above survey, 
the sum of the distances is 17 chains and 9 links ; the error of 
latitude 3, and the error of departure 11, may be distributed 
as in the two columns " correction." Notice that as the 
southings are less than the northings, a correction applied to 
a southing is marked -f, and one applied to a northing — 
The same principle is used in the signs of the corrections of 
departures. 

This mode of distributing the error is well enough uuder 
the circumstances stated, but the surveyor who has been over 
the whole line with chain and compass usually knows that 
the error is probably due to the sides, in a different ratio from 
that of their lengths. On a short side there may be many ob- 
structions and difficulties, none of which are met on a long 
side. The skilful surveyor distributes the error according to 
his judgment of all the circumstances. 

The figures in the columns of balanced latitudes and de- 
partures are found by applying the corrections to the previous 
columns. They are " balanced" because the sum of the 
northings equals that of the southings, etc. The first latitude 
is marked with the negative sign, because it belongs to an area 
which is to be substracted in order to complete the calculation, 
that is the triangle AGB. 

The signs in this column are subject to this rule:— Make 
the first latitude negative, also all that are in the same direc- 
tion as the first, and those in the opposite direction positive. 

The balanced departures of those sides which tend or de- 
part from the prime meridian are marked -f , and those which 
tend towards it — . The reasonableness of these si^ns is obvi- 



16 SURVEYING. 

ous at the next step, as the departures are used to fin J the 
onble meridian distances, marked " D. M. D." 

The double meridian distance of a side is twice the dis- 
tance of the centre of that side from the prime meridian ; or, 
it is the base of the triangle or the sum of the bases of the 
trapezoid corresponding to that side. For the side AB, it is 
GB ; for the side BC, it is GB-f-HC ; etc. 

Theorem. Each double meridian distance is equal to the 
sum of its own departure, increased by the preceding depart- 
ure, and the preceding double meridian distance. 

The first double meridian distance is manifestly equal to 
the first departure, for the base of the triangle AGB consti- 
tutes both ; and there is no preceding departure, etc. to add. 

To prove the theorem in other cases, draw BN from B 
perpendicular to the line HO. Then NO is the departure of 
the side BC, and as GB is equal to HN, we have CH -+- 
BG = ON + Nil + BG. Again, draw DP perpendicular 
t) CH. Then CP is the departure of CD, and is negative, 
and the third D. M. D. is CH + DJ. This is equal to — 
CP h- CN + CH + BG, as is evident. 

We have now the altitudes of every triangle and trapezoid, 
that is the latitudes, and we have the bases. The product of 
the base, or the sum of the bases, by the altitude, gives the 
double area (Geom. Art. 386 and 392). Subtracting the sum 
of the exterior areas from the sum of those which include the 
whole figure, (that is, in this case the South areas from the 
North) the remainder is twice the area of the field, expressed 
in square chains. Dividing this by 20, reduces it to acres. 

The student must bear in mind that the prime meridian 
might be on the East, and the surveyor might have gone 
around the field in the opposite direction. Either of these 
would cause some of the signs to be changed. 

Exercises. — 1. Make the plat and calculation of acreage of 
the lot having this boundary : Beginning at a certain corner, 
thence North 45° East nine chains and thirty links, thence South 
60° E:\st eleven chains and five links, thence South 20° West ten 



SURVEYING. 17 

chains and ninety links, thence North 31° West nine chains and 
forty links to the place of beginning. 

2. Divide this lot into equal parts by a line beginning at 
the middle of the first side; find the bearing and length of this 
dividing line, and the segments of the other side which it reaches 
and divides. 

3. Make the plat and calculation from this survey : From 
point of beginning North 50°J East sixty-six rods, thence South 
68°i East fifty-six rods and twenty links, thence South 9°f East 
thirty-three rods and twenty links, thence South 21° West 
twenty-seven rods and nine links, thence South 73° \ West 
forty-nine rods and sixty links, thence North 78° x f West thirty- 
nine rods and one link, thence North 17° West forty-six rods 
and fourteen links to the place of beginning. 

4. Divide the tract of land just described into two equal 
parts by a line running East and West. 

5. Find the number of hectares within the following boun- 
dary : 

meters. 



1 


S. 


58°* 


W. 


292.7 


2 


N. 


34° 


W. 


198. 


3 


N. 


81°i 


w. 


212.4 


4 


X. 


36°i 


E. 


247.3 





N. 


703 

' 4 


E. 


115.8 


6 


N. 


79°^ 


E. 


154. 


7 


S. 


86°f 


E. 


205.5 


8 


s. 


12°|- 


W. 


181.5 


9 


s. 


25° 


E. 


219.2 



6. On the plat of the last field, draw a line from the end of 
the second side, leaving fifteen hectares to the West of it. Find 
the bearing and length of this line. 

7. In the records of field notes, if the bearing and distance 
of one side is lost, how can they be calculated, supposing all that 
remain to be accurate? 












TRAVERSE TABLE. 








Bear'g. 


Latitude. 


Departure 


o 

1 

2 


Bear'g. 
o 

23 


Latitude. 


1 
Departure 


o 


foooo 


0.0087 


$.9205 0.3907 


O 

67 


1 


9998 


0175 


89 


i 

2 


9171 


3987 


2 


1 

2 


9997 


0262 


i 

2 


24 


9135 


4067 


6G 


2 


9994 


0349 


88 


i 

2 


9100 


4147 


i 

2 


i 

2 


9990 


0436 


i 

2 


25 


9063 


4226 


65 


3 


9986 


0523 


87 


i 

2 


9026 


4305 


i 

2~ 


i 

2 


9981 


0610 


i 

2 


26 


8988 


4384 


64 


4 


9976 


0698 


86 


i 

2 


8949 


4462 


JL 
2 


i 


9969 


0785 


i 

2 


27 


8910 


4540 


63 


5 


9962 


0872 


85 


i 

2 


8870 


4617 


4 


i 

2 


9954 


0958 


i 

2 


28 


8829 


4695 


62 


6 


9945 


1045 


84 


i 


8788 


4772 


1 

2 


i 


9936 


1132 


i 

2 


29 


8746 


4848 


61 


7 


9925 


1219 


83 


i 

2 


8704 


4924 


i 

2 


i 


9914 


1305 


i 

2 


30 


8660 


5000 


60 


8 


9903 


1392 


82 


i 

2 


8616 


5075 


i 

2 


i 


9890 


1478 


i 

2 


31 


8572 


5150 


59 


9^ 


9877 


1564 


81 


i 

2 


8526 


5225 


i 

2 


i 


9863 


1650 


i 

2 


32 


8480 


5299 


58 


2j 

10 


9848 


1736 


80 


i 

2 


8434 


5373 


i 

2 


* 


9833 


1822 


i 

2 


33 


8387 


5446 


57 


11 


9816 


1908 


79 


i 

2 


8339 


5519 


i 


1 

Q 


9799 


1994 


i 

2 


34 


8290 


5592 


56 


12 


9781 


2079 


78 


i 
<> 


8241 


5664 


i 

"5" 


2 

13 


9763 


2164 


i 

2 


35~ 


8192 


5736 


55 


9744 


2250 


77 


i 

2 


8141 


5807 


i 

2 


i 

o 


9724 


2334 


i 

2 


36 


8090 


5878 


54 


14 


9703 


2419 


76 


i 

2 


8039 


5948 


i 


i 

2 


9681 


2504 j \ 


37 


7986 


6018 


53 


15 


9659 


2588 


75 


i 

2 


7934 


6088 


i 

2 


i 


9636 


2672 


i 

2 


38 


7880 


6157 


52 


16 


9613 


2756 


74 


i 

2 


7826 


6225 


i 

2 


i 


9588 


2840 


i 

2 


39 


7771 


6293 


51 


17 


9563 


2924 


73 


i 

2 


7716 


6361 


i 

2 


i 


9537 


3007 


i 

9, 


40 


7660 


6428 


50 


18 


9511 


3090 72" 


i 

35" 


7604 


6494 


i 

2 


i 


9483 


3173 


1 

2 


41 


7547 


6561 


49 


19 


9455 


3256 


71 


i 

2 


7490 


6626 


i 

2 


i 

o 


9426 


3338 


i 

2 


42 


7431 


6691 


48 


2Cf 


9397 


3420 


70 


i 

2 


7373 


6756 


l 


i 


9367 


3502 


i 

2 


43 


7314 


6820 


47^ 


21 


9336 


3584 


69 


i 

2 


7254 


6884 


i 

2 


i 


9304 


3665 


i 


44 


7193 


6947 


46 


22 


9272 


3746 


68 


£ 


7133 


7009 




i 

2 


9239 


3827 


2 


45 


7071 


7071 


15" 




Departure 


Latitude. 


Bear'g. 


Departuer 


Latitude. 


Bear'g. 



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